Quantum mechanics on phase space and teleportation (original) (raw)
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Discrete Wigner functions and the phase-space representation of quantum teleportation
Physical Review A, 2002
We present a phase space description of the process of quantum teleportation for a system with an N dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.
Classical communication and non-classical fidelity of quantum teleportation
Quantum Information Processing, 2013
Physics and applied mathematics unit, Indian statistical unit, 203 B.T. Road, India In quantum teleportation, the role of entanglement has been much discussed. It is known that entanglement is necessary for achieving non-classical teleportation fidelity. Here we focus on the amount of classical communication that is necessary to obtain non-classical fidelity in teleportation. We quantify the amount of classical communication that is sufficient for two one-bit and one two-bits noisy classical channels for non-classical fidelity and we also find the necessary amount of classical communication for isotropic transformation. PACS numbers: 03.67.Hk, 03.67.-a, 03.65.Aa
Fidelity and information in the quantum teleportation of continuous variables
Physical Review A, 2000
Ideally, quantum teleportation should transfer a quantum state without distortion and without providing any information about that state. However, quantum teleportation of continuous electromagnetic field variables introduces additional noise, limiting the fidelity of the quantum state transfer. In this article, the operator describing the quantum state transfer is derived. The transfer operator modifies the probability amplitudes of the quantum state in a shifted photon number basis by enhancing low photon numbers and suppressing high photon numbers. This modification of the statistical weight corresponds to a measurement of finite resolution performed on the original quantum state. The limited fidelity of quantum teleportation is thus shown to be a direct consequence of the information obtained in the measurement.
Teleportation of Continuous Quantum Variables: A New Approach
arXiv (Cornell University), 2009
Teleportation of optical field states (as continuous quantum variables) is usually described in terms of Wigner functions. This is in marked contrast to the theoretical treatment of teleportation of qubits. In this paper we show that by using the holomorphic representation of the canonical commutation relations, teleportation of continuous quantum variables can be treated in complete analogy to the case of teleportation of qubits. In order to emphasize this analogy, short descriptions of the basic experimental schemes both for teleportation of qubits and of continuous variables are included. We conclude our paper with a brief discussion of the effectiveness of our description of continuous variable teleportation and of the role of localization of quantum states in teleportation problems.
On statistical and deterministic quantum teleportation
Journal of Physics A: Mathematical and General, 1998
We generalize quantum teleportation to, what we call, statistical teleportation utilizing previous results on distant preparation, and on the basic ingredient entities of an entangled composite-system state vector. Our main result is 'the central theorem', establishing a simple necessary and sufficient condition for the crucial entity: the event that the sender of a pure quantum state has to measure in the first step of the two-step (and two-laboratory) teleportation procedure. We derive numerous consequences especially for deterministic teleportation (a special case of statistical teleportation), which is a direct generalization of the known quantum teleportation. Detailed further generalization to proper and improper mixtures is investigated. Finally, it is shown that extension to teleportation with nonlinear distant preparation is not possible unless the idea of teleportation is essentially changed.
Non-ambiguity quantum teleportation protocol
2019
Teleportation is the most important and impactful tool in the arsenal of quantum communications with a particular projection on quantum internet. We propose a non-ambiguity alternative to the original teleportation protocol, which completely eliminates the classical-disambiguation-channel used by the original version. Experimental evidence on a quantum platform, via IBM cloud, is provided to demonstrate its performance. Introduction.-Since the publication of the famous paper of Bennett et al [1], quantum teleportation has gained a central position in the world of quantum communications [2], for all that it represents and implies. This protocol consists of the following steps: (i) the generation and distribution of an entangled pair, in order to build a quantum channel between Alice and Bob. (ii) Alice receives the qubit to be teleported, which when interacting with one of the elements of the entangled pair gives rise to an ambiguous state, that is, a sum in which the original state is involved in four ways at once. (iii) Alice must make a measurement on that state, whose result is absolutely random. This measurement eliminates ambiguity, entanglement and also the original state, otherwise the No-Cloning Theorem [3] would be violated with each teleportation, which we know does not happen under any point of view. (iv) Alice transmits to Bob the result of the detection process via a classical channel, subject to the restrictions of the Einstein-Podolsky-Rosen (EPR) paradox [4], and therefore of the Special Relativity [5], which states that nothing can travel faster than light, implying that teleportation as a whole cannot be a process of instant transmission of useful information at all. (v) Bob applies a unit transformation based on the classical bits sent by Alice in order to reconstruct the teleported state. The distribution of the entangled pair from which each teleportation process is inaugurated is also carried out through a classical channel, usually using optical-fiber [6]. This procedure requires repeaters every approximately 50 km due to the optical properties of the fiber, for example: the absorption, the refractive index, and the reduced speed to which the entangled element travels (2/3 of speed of light in vacuum) which would make all teleportation efforts impossible over long distances by land without the use of quantum repeaters [7]. In some cases [8], an optical link based on a canontelescope pair is used, which does not require repeaters, as long as the eye contact between both elements is maintained. Teleportation uses two classical channels: the first one for the distribution of the entangled pair, and the second one between Alice and Bob to be used in the transmission of the measurement result made by Alice. Consequently, the elimination of this second channel, which represents the central idea of this work, does not imply in the least that the new teleportation protocol is instantaneous as a whole and thus collides with the Special Relativity [5], given that there is still the first classical channel for the distribution of the entangled pair, which gives rise to the quantum channel. Based on what has been said so far, a question automatically arises: what is the impact of the second classical channel in the context of quantum communications? We will answer it with an example. If we use a quantum key distribution (QKD) protocol based on entanglement [9], we will have several channels at once: a first classical channel for the distribution of the entangled pair, which generates the quantum channel on which the public key will be teleported, the quantum channel generated as a result of the previous step, a second classical channel through which Alice transmits to Bob the result of her measurement, and a third classical channel on which the ciphered text travels, and which is encrypted by means of the teleported public key. If this architecture was intervened by a hacker, he would not be able to obtain the key that is teleported through the quantum channel, due to the fact that this channel is inaccessible to him, since an entanglement link is an intrinsically monogamous mean [10], that is, no third party can intervene without an initial consent of Alice and Bob, or what is the same, if at the time of the generation and distribution of the entangled elements no
An investigation of the transfer dynamics of quantum teleportation by weak measurement statistics
Journal of Physics A: Mathematical and Theoretical, 2013
We explore the mechanism of quantum teleportation by analyzing the weak measurement statistics post-selected by the result of the Bell measurement for the joint system composed of the input A and the spatially separated output B. It is shown that the weak measurement statistics observed before the Bell measurement includes correlations which relate every physical property in the input A to a corresponding physical property in the output B. The Bell measurement thus identifies the accidental relation between A and B already present in the quantum fluctuations of the input state. Significantly, this relation applies to all physical properties equally, and is completely independent of the input state. Teleportation therefore copies all physical properties of input system A to output system B, irrespective of whether the input state is an eigenstate of the property or not.
Physical Review Letters, 1998
We report on a quantum optical experimental implementation of teleportation of unknown pure quantum states. This realizes all of the nonlocal aspects of the original scheme proposed by Bennett et al. and is equivalent to it up to a local operation. We exhibit results for the teleportation of a linearly polarized state and of an elliptically polarized state. We show that the experimental results cannot be explained in terms of a classical channel alone. The Bell measurement in our experiment can distinguish between all four Bell states simultaneously allowing, in the ideal case, a 100% success rate of teleportation. [S0031-9007(97)05275-7] PACS numbers: 03.65.Bz, 03.67. -a, 42.50. -p, 89.70. + c In Ref. [1], Bennett et al.